More recently, theoretical works have sought to merge the principles of the modeling of the walk reviewed above with those of the modeling of the travel in which the behavior of each leg is likened to that of a spring with a given coefficient of extension and of length at rest.
These concepts have not however been applied with success to control the movement of robots over a long period. One of the reasons for this incapacity is probably that the principle of the inverse pendulum has hitherto been usefully applied only to the objects to which an external source imparted sufficient kinetic energy to ensure the forward progression beyond a few steps. The motorization of the hips is not in fact sufficient, except in cases such as that of a robot skating on ice, to communicate to a robot sufficient energy to compensate for the losses connected to the friction of the feet on the ground.
Most of the designers of robots articulated on limbs, notably the Japanese manufacturers such as Honda and Sony, have, for the driving of the walk, made use of various embodiments of a central concept called “Zero Moment Point”, or ZMP. According to this concept, a determination is first of all made of the trajectory that the ZMP needs to have in a coordinate system connected to the ground to satisfy the dynamic balance conditions all along a trajectory planned according to walking direction and speed objectives. Then, the positions of the terminations and articulations of the robot are computed in the same coordinate system connected to the ground at each instant by inverse transformation of the equations determining the respective positions of the ZMP and of said terminations and articulations. This approach notably presents the following drawbacks: i) it presupposes a knowledge of the topography of the ground to be able to position, at any moment, the ZMP and the useful points of the robot in a coordinate system connected to the ground; ii) it entails a complete trajectory planning computation, which is extremely demanding in terms of computation power. Various improvements of the basic concept have been proposed over the years to limit the drawbacks of this approach. However, to date, no improvement has been able to totally eliminate them.